The previous reply is confused.
Each year you will decide whether or not to elect the remittance basis on your UK tax returns or to file on the arising basis.
You will presumably choose whichever gives you the lowest tax globally. For most US persons (but not all) the arising basis is the lowest after claiming treaty resourcing on the US return.
If you elect the remittance basis you would only pay UK tax on US source income oir gains if remitted to the UK. If on the arising basis, you would pay UK income at rates of up to 50% on most dividends, capital gains distributions and capital gains. Losses cannot be set against gains for non-reporting funds.